AMP MATH VIDEO LIBRARY
1. Fermat's Last
Theorem-The Theorem and its Proof: An Exploration of Issues and Ideas.
"`Fermat Fest: The Video' successfully brings to life one of the most dramatic episodes in the history of mathematics. A superb cast of speakers and a lively soundtrack featuring such hits as Tom Lehrer's `There's a delta for every epsilon' and `That's mathematics' (with original lyrics to celebrate Wiles' achievement) make this an ideal entertainment and educational value for the undergraduate classroom, mathematical parties, and indeed for the whole family ... All in all, `Fermat Fest: The Video' definitely rates an enthusiastic 'thumbs-up', and is sure to delight mathematicians and non-scientists alike."
-- Mathematical Reviews
Description
In July 1993,
just three weeks after Andrew Wiles's announcement of
a proof of Fermat's Last Theorem, the Mathematical Sciences Research Institute
hosted a special celebration in
Moderator: Will Hearst; Speakers: Robert Osserman, Lenore Blum, Karl Rubin, Kenneth Ribet, John H. Conway; Panelists: Lenore Blum, John H.
Conway, Lee Dembart, Kenneth Ribet;
Musician: Morris Bobrow.
This tape is produced by MSRI and
distributed by the American Mathematical Society.
Publisher: MSRI
Distributor: American Mathematical Society
Series: Selected Lectures
Publication Year: 1994
ISBN: 0-9639903-0-6
Duration: 90 minutes
2. Modular Elliptic
Curves and Fermat's Last Theorem
"Accessible to advanced undergraduates and graduate students with some background in algebra and number theory."
-- Zentralblatt MATH
Description
In 1637, Pierre de Fermat wrote his legendary marginal comment that xn+yn=zn has no solution in positive integers when n≥3. Fermat's Last Theorem has eluded proof over the centuries, stimulating a great deal of mathematical development. In 1993, Andrew Wiles announced his proof of this celebrated theorem. Wiles's main result, a special case of the Taniyama Conjecture, relies on a wide range of mathematical tools developed over the past ten years. A crucial link was a 1986 theorem that the Taniyama Conjecture implies Fermat's Last Theorem, proved by Kenneth Ribet, who gives the two lectures on this videotape. Presented just weeks after Wiles's now-historic announcement, these expository lectures describe the main ingredients in Wiles's results. The lectures would be accessible to advanced undergraduates and graduate students with some background in algebra and number theory.
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Selected Lectures
Publication Year: 1993
ISBN: 0-8218-8087-X
Duration: 100 minutes
3. A Conversation
with Paul Halmos
Description
Halmos, mathematician, writer, lecturer, and teacher extraordinaire, begins by telling his audience, "I'm scared stiff!" In this candid interview, Halmos in his inimitable fashion, talks about teaching, students, the value of experiment in teaching, calculus reform, the Moore Method, changes in teachers and students over the last twenty years, and personal reminiscences of famous mathematicians he has known. A must for all Halmos' fans.
Publisher: Mathematical Association
of
Duration: 40 minutes
4. N is a Number: A
Portrait of Paul Erdos
This well-shot program is an excellent choice for mathematics students and others familiar with Erdos' accomplishments.
-- Booklist
I strongly
believe that most high school students, science and mathematics teachers, and
administrators will enjoy watching this films. I give
it two thumbs up!
-- The Mathematics Teacher
Description
A man with no
home and no job, Paul Erdos was the most prolific
mathematician who ever lived. Universally revered among mathematicians, Erdos, who was born in
N is a Number, a
documentary filmed in England, Hungary, Poland and the United States over four
years, presents Erdos's mathematical quest in its
personal and philosophical dimensions, and the tragic historical events that
molded his life. N is a Number was made with support from the American
Mathematical Society, Film Arts Foundation, the Heineman
Foundation, the Mathematical Association of America and the National Science
Foundation's Informal Science Education Program.
Duration: 58 minutes
5. Let Us Teach Guessing. George Pólya
Description
In a remarkable tour de force, Pólya shows us how to teach guessing. In this classic film, master teacher Pólya leads an undergraduate class to discover the number of parts into which 3-space is divided by five arbitrary planes.
1966, color, 61 minutes
6. MAA Calculus Films in Video Format
Description
This series of films was produced by the MAA in the late 60s.The films range in style from informational scripted graphics with hand-painted gels to humorous cartoons. Some films present informal introductions to topics from calculus; others include precise, detailed investigations. Each tape is approximately 60 minutes in length.
Tape 1:
A Function is a Mapping
Continuity of Mappings
Limit
I Maximize
Theorem of the Mean Policeman
60 minutes
Tape 2:
The Definite Integral as a Limit
Fundamental Theorem of the Calculus
What is Area?
60 minutes
Tape 3:
Area Under a Curve
The Definite Integral
The Volume of a Solid of Revolution
Volume by Shells
Infinite Area
60 minutes
7. Careers in Mathematics
Description
The
"Careers in Mathematics" video contains interviews with
mathematicians working in industry, business and government. The purpose of the
video is to allow the viewer to hear from people working outside academia what
their day-to-day work life is like and how their background in mathematics
contributes to their ability to do their job. Interviews were conducted on site,
showing the work environment and some of the projects mathematicians
contributed to as part of multidisciplinary teams. People interviewed come from
industrial based firms such as Kodak and Boeing, business and financial firms
such as Price Waterhouse and D. E. Shaw & Co., and government agencies such
as the National Institute of Standards and Technology and the
Careers in Mathematics was developed jointly by the American Mathematical Society (AMS), the Society for Industrial and Applied Mathematics (SIAM), and the Mathematical Association of America (MAA).
Publisher: American Mathematical Society,
Society for Industrial and Applied Mathematics, Mathematical Association of
Distributor: American Mathematical Society
Publication Year: 2001
ISBN: 0-7872-6790-2
Duration: 35 minutes
8. Preparing for Careers in Mathematics
Organized by: Annalisa
Crannell,
Speakers: Steven J. Altschuler, Microsoft Corporation, Redmond, WA, William Browning, Applied Mathematics, Inc., Gales Ferry, CT, Ray E. Collings, DeKalb College, Clarkston, GA, Margaret Holen, Lehman Brothers, New York, NY, Sandra L. Rhoades, Keene State College, NH, James R. Schatz, National Security Agency, Ft. George G. Meade, MD, Anita Solow, DePauw University, Greencastle, IN, and Francis Edward Su, Harvey Mudd College, Claremont, CA.
Description
This video
presents an edited version of a panel discussion that took place at the Joint
Mathematics Meetings in
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: AMS-MAA Joint Lecture Series
Publication Year: 1997
ISBN: 0-8218-0839-7
Duration: 30 minutes
9. Introduction to Geometric Probability. Gian-Carlo
Rota
"This
lecture examines the notion of invariant measure from a fresh viewpoint. Master
expositor Gian Carlo-Rota shows how, starting with a
few simple axioms, one can concoct new invariant measures and explore their
properties. One set of such measures, known as the intrinsic volumes, are quite
new and still somewhat mysterious. However, they have intriguing probabilistic
interpretations and in fact can be shown to form a basis for the space of all
continuous invariant measures.
-- Zentralblatt
MATH
"Since this
remarkable member of the mathematical community died on
-- Mathematical Reviews
Description
This lecture
examines the notion of invariant measure from a fresh viewpoint. The most
familiar examples of invariant measures are area and volume, which are
invariant under the group of rigid motions. Master expositor Gian-Carlo Rota shows how, starting with a few simple
axioms, one can concoct new invariant measures and explore their properties.
One set of such measures, known as the intrinsic volumes, are quite new and
still somewhat mysterious. However, they have intriguing probabilistic
interpretations and in fact can be shown to form a basis for the space of all
continuous invariant measures.
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Publication Year: 1999
ISBN: 0-8218-1351-X
Duration: 60 minutes
10. Interview with
Description
In this one-hour
interview, I. M. Gelfand, one of the major
mathematicians of the century, discusses his mathematics, his inspirations, and
his major achievements. He also touches on his work in biology and education,
two areas in which he has had an important impact. The interview was held
during the Joint Mathematics Meetings in
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Selected Lectures
Publication Year: 1993
ISBN: 0-8218-8084-5
Duration: 60 minutes
11. Some Mathematics of Baseball. Henry O. Pollak
"Pollack is lively, entertaining and engaging as he steps through the problems. His methods of using the statistics of a great game to demonstrate mathematics will surely delight anyone with even the remotest interest in baseball ... this was far and away the most interesting analysis of world series events that I have seen in four decades of following the sport ... an excellent way to teach algebra or probability by demonstrating a real-world problem with serious consequences."
-- Mathematics and Computer Education
Description
Get out your mitts, your baseballs, your bats--and your calculators? This videotape of the 1991 Pi Mu Epsilon J. Sutherland Frame Lecture presents a delightful tour through a myraid of ways of applying mathematics to baseball; and the best thing is, you don't have to be a baseball fan to enjoy it! Witty, engaging, and indefatigable, Pollak pursues his topic with a passion: "Once this gets in your blood, you just don't stop!" He doesn't just stick to those dry statistics that sportswriters bandy about--he actually builds models to analyze the game and discusses why the models work in some ways and don't in others. Well-paced and lucid, with a judicious use of numbers and calculations, the lecture is accessible to students having a familiarity with basic probability theory. It makes an excellent classroom enrichment tool, especially when shown around the time of the World Series.
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Selected Lectures
Publication Year: 1993
ISBN: 0-8218-8083-7
Duration: 60 minutes
12. Descartes and Problem Solving. Judith Grabiner
Description
This videotape captures a lively, vivid, and meticulously researched lecture by the noted mathematical historian Judith Grabiner. In looking at Descartes' approach to problem solving, Grabiner brings into focus his general philosophy that, unless one has method, one will never discover anything useful. His general method was to reduce a geometric problem to an algebraic one and then construct a curve that solves the algebraic problem. Grabiner demonstrates how Descartes used this method in a particular situation. Connecting this mode of thinking to the history that preceded Descartes, she shows how he combined, extended, and exploited earlier methods. The lecture is accessible to undergraduates with an interest in mathematics and would make a fine supplement to a course in mathematics or mathematics history.
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Selected Lectures
Publication Year: 1992
ISBN: 0-8218-8069-1
Duration: 60 minutes
13. Pedagogical Peeves and Other
Complaints of Age: Crazy Al, Still Teaching Calculus after All These Years. Al Novikoff
Description
At times wildly funny, always thought-provoking, this videotaped lecture provides insight into some of the central problems in teaching and learning calculus. Although such student foibles as f(x+y)=f(x)+f(y) make Novikoff want to "sue in the World Court," he also has great sympathy for the genuine confusion students feel when confronted with supposedly clear mathematical explanations that actually obscure the basic ideas of the subject. Presenting a smorgasbord of specific examples, Novikoff builds his basic point: mathematics makes sense, but textbooks and teachers often don't. His examples not only can help teachers of calculus improve their presentations of particular topics, but also reflect a teaching philosophy that emphasizes responding to students, what they know and what they don't, what makes sense to them and what doesn't. Anyone who teaches mathematics will appreciate this engaging and insightful lecture.
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Selected Lectures
Publication Year: 1992
ISBN: 0-8218-8071-3
Duration: 60 minutes
14. The Mysteries of Space. Michael Atiyah,
"This video tape provides a good opportunity to enjoy the vivid lecturing style of Sir Michael Atiyah."
-- Zentralblatt
MATH
Description
From the
earliest times, the geometry of space has been intimately involved with
physics. As science has evolved and our understanding has deepened, the
relations between geometry and physics have become subtler and more complex. At
the present time, fundamentally new ideas from both areas are dramatically
altering conceptions about the nature of the universe. In this videotaped
presentation, Sir Michael Atiyah, one of the foremost
mathematicians of this century, discusses some of the recent deep connections
that have been discovered between mathematics and quantum physics. Starting with the viewpoints of
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Selected Lectures
Publication Year: 1992
ISBN: 0-8218-8076-4
Duration: 60 minutes
15. Algebra as a Means of Understanding Mathematics.
"Accessible to those at the level of an advanced undergraduate."
-- Mathematical Reviews
Description
What is the real nature of algebra? How does algebra help us to gain insight into other areas of mathematics? Saunders MacLane probes these and other questions. In a lecture that ranges from categories to braids, from tensor products to spectral sequences, MacLane shows how algebra forms a common thread uniting them all. The lecture is accessible to advanced undergraduates. (Columbus, OH, 1990)
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: AMS-MAA Joint Lecture Series
Publication Year: 1991
ISBN: 0-8218-8057-8
Duration: 60 minutes
16. Case Studies of Political Opinions Passed Off as Science and Mathematics.
Serge Lang
"An excellent choice for a colloquium or seminar meeting, this videotape exposes some of the bad things that can happen in the academic world ... good viewing for undergraduates considering a scholarly career."
-- Mathematics and Computer Education
Description
In this
fascinating videotaped presentation, Serge Lang discusses his nationally
publicized battle against what he sees as quantitative verbiage used by some
people in the social sciences to pass off political opinions as science. The
central part of the lecture focuses on some works of Samuel Huntington, a
well-known political scientist who was rejected by the National Academy of
Sciences, partly as a result of Lang's campaign against him. Quoting from
original sources, Lang documents how Huntington and other authors not only
misused what some people call mathematics by assigning numerical values to
various social phenomena (such as a "frustration index" for a
society), but also misrepresent historical facts. Lang describes reactions in
the social science community, in the press, and those of several students who
used
Never one to shy away from controversy over causes he believes in, Lang devoted a great deal of time and energy into what he sees as a crucial fight for standards and integrity in academia. His story raises challenging questions about the standards that scholars set for themselves, their institutions, and their colleagues. The lecture would be suitable for students and scholars in any academic discipline. A writeup of the talk, with references, is included. (Boulder, CO, 1989)
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: AMS-MAA Joint Lecture Series
Publication Year: 1991
ISBN: 0-8218-8037-3
Duration: 60 minutes
17. Von Neumann Algebras in Mathematics and
Physics.
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: ICM Series
Publication Year: 1991
ISBN: 0-8218-8053-5
Duration: 60 minutes
18. ax2
+ hxy + cy2 = n. John H. Conway
Description
The quadratic
forms of the type in the title of this lecture lead to a beautiful picture in
the hyperbolic plane--a picture that not only allows for understanding of the
deeper properties of these forms but also leads to an algorithm for their
solution. Taking viewers on a trip down "the river," with a forest of
positive integers on one side, and negative integers on the other,
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: AMS-MAA Joint Lecture Series
Publication Year: 1990
ISBN: 0-8218-8027-6
Duration: 60 minutes
19. Matrices I Have Met. Paul Halmos
Description
Imbued with Halmos's inimitable charm and wit, this is not so much a lecture as a friendly chat, and will spark the interest of anyone with even a minimal understanding of matrix algebra. (New Orleans, LA, 1986)
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: AMS-MAA Joint Lecture Series
Publication Year: 1986
ISBN: 0-8218-8017-9
Duration: 60 minutes
20. In Search of Symmetry. William Browder
"The reviewer recommends enthusiastically this tape to the mathematical community, in particular those interested in algebraic topology and its applications to transformation groups."
-- Zentralblatt
MATH
Description
William Browder served as President of the American Mathematical Society during 1990-1991. This videotape contains his Retiring Presidential Address--which combined short remarks about his presidency with a mathematical lecture--preceded by an informal interview in which he discusses a range of topics, including public awareness of mathematics and his interest in music. The lecture discusses the action of finite groups on manifolds, exploring the question of how large a finite group can effectively act on a given manifold (here, "effectively" means that there is no subgroup that fixes everything). A related question is, what kind of spaces have the given manifold as a covering space? Beginning with the historical roots of these questions, Browder concentrates on familiar examples such as the sphere, the n-sphere, or a product of spheres of different dimensions. The lecture is accessible to mathematics majors with background in algebraic topology. The interview segment provides a fine complement to the lecture.
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Selected Lectures
Publication Year: 1994
ISBN: 0-8218-8091-8
Duration: 90 minutes
21. The
Description
In this film
shot in his classroom,
1966, color, 55 minutes
22. The Story of Pi
Description
Although π is the ratio of circumference to diameter of a circle, it appears in many formulas that have nothing to do with circles. Animated sequences dissect a circular disk of radius r and transform it to a rectangle of base π r and altitude r. Animation shows how Archimedes estimated π using perimeters of approximating polygons.
Duration: 24 minutes
23. John von Neumann. A Biography
Description
Rare footage and photographs of the legendary von Neumann are to be found in this film biography. Halmos, Morgenstern, Teller, Wigner, and Ulam contribute insights about and memories of Johnny.
1966, b&w, 63
minutes
24. A New Look at Knot Polynomials. Joan Birman
"An excellent introduction to the theory of knots."
-- Zentralblatt
MATH
Description
This videotape
combines a lecture with an informal interview to bring out the fascination of
the subject of knot polynomials as well as a personal view of the field from
one of its leaders. In the interview portion of the tape, Birman
discusses her role in the discovery of the celebrated Jones polynomial, how she
got started in knot theory, and some of the changes she has seen in the field. Birman's lecture, widely praised at the 1992 Joint
Mathematics Meetings in
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: AMS-MAA Joint Lecture Series
Publication Year: 1993
ISBN: 0-8218-8078-0
Duration: 60 minutes
25. The Teaching of Calculus: Careful Changes. Gilbert Strang
Description
Well known for his textbooks and his attention to students, Gilbert Strang has some novel ideas about how to teach calculus. In this insightful videotaped lecture, Strang discusses how concepts that commonly confuse students can be used as springboards to better understanding. For example, students often confuse the functions x3 and 3x. In fact, for some values of x, the graphs of these two functions look very similar and actually cross in two places. Using a computer to plot such functions avoids "flooding the course with numbers", as Strang puts it, and improves the students' ability to visualize. He shows how looking at integration numerically on a computer can help students to better understand infinitesimals. He also presents computer "experiments" with iterations of functions that produce surprising and intriguing results. This videotape is useful to anyone interested in new ways to teach calculus and mathematics in general.
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Selected Lectures
Publication Year: 1992
ISBN: 0-8218-8068-3
Duration: 60 minutes
26. George Lusztig, Intersection cohomology methods in representation theory
Talk at the International Congress of
Mathematicians 1990
Acknowledgment
of support:
Supported
by the National Science Foundation under Grant No. HRD-0331537.